\newproblem{lay:4_5_28}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.5.28}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Show that the space $C(\mathbb{R})$ of all continuous functions defined on the real line is an infinite-dimensional space.
}{
  % Solution
	In the previous exercise we showed that the space of polynomials $\mathbb{P}$ is infinite-dimensional. Since all polynomials are continuous functions on 
	the real line we have $\mathbb{P}\subseteq C(\mathbb{R})$. Consequently, $C(\mathbb{R})$ must be infinite-dimensional since its dimension cannot be smaller
	than the dimension of $\mathbb{P}$.
}
\useproblem{lay:4_5_28}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
